Sums of four generalized polygonal numbers of almost prime length

TL;DR

This paper proves that large integers can be expressed as sums of four generalized polygonal numbers with parameters having a limited number of prime factors, under certain modular restrictions.

Contribution

It establishes a representation result for sums of four generalized polygonal numbers with parameters constrained by prime factor count and modular conditions.

Findings

Large integers are representable as such sums under the given restrictions.

Parameters can have at most 988 prime factors in these representations.

Representation holds for sufficiently large integers.

Abstract

In this paper, we consider sums of four generalized polygonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restriction on m modulo 30, we show that for n sufficiently large, it can be represented as such a sum, where the parameters are restricted to have at most 988 prime factors.